Stokes–Einstein relation
E31544
The Stokes–Einstein relation is a fundamental equation in statistical physics that links the diffusion coefficient of a particle in a fluid to its size, the fluid’s viscosity, and temperature.
All labels observed (1)
| Label | Occurrences |
|---|---|
| Stokes–Einstein relation canonical | 2 |
How this entity was disambiguated
This entity first appeared as the object of triple T243762 — resolving that mention is where its identity was fixed. The disambiguator weighed these candidate entities and picked the highlighted one (or “None”, minting a new entity). This is how homonymy is resolved: the same surface form can point to different entities.
NED1
Entity disambiguation (via context triple)
gpt-5-mini-2025-08-07
Target entity: Stokes–Einstein relation Context triple: [Einstein–Smoluchowski relation, relatedConcept, Stokes–Einstein relation]
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A.
Einstein–Smoluchowski relation
The Einstein–Smoluchowski relation is a fundamental equation in statistical physics that links the diffusion coefficient of particles undergoing Brownian motion to their mobility and thermal energy.
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B.
On the Motion of Small Particles Suspended in Liquids at Rest Required by the Molecular-Kinetic Theory of Heat
"On the Motion of Small Particles Suspended in Liquids at Rest Required by the Molecular-Kinetic Theory of Heat" is Albert Einstein’s 1905 paper that provided a theoretical explanation of Brownian motion, offering strong evidence for the existence of atoms and molecules.
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C.
Brownian motion
Brownian motion is the random, jittery movement of microscopic particles suspended in a fluid, whose explanation provided key evidence for the existence of atoms and the molecular nature of matter.
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D.
Fokker–Planck equation
The Fokker–Planck equation is a partial differential equation that describes the time evolution of the probability density function of a stochastic (random) process, such as Brownian motion.
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E.
Langevin dynamics
Langevin dynamics is a stochastic approach to modeling the motion of particles in a fluid by combining deterministic forces with random thermal fluctuations, often used to simulate Brownian motion and other nonequilibrium processes.
- F. None of above. chosen
- G. Unsure - the case is ambiguous/there is not enough information to decide.
NED2
Entity disambiguation (via description)
gpt-5-mini-2025-08-07
Target entity: Stokes–Einstein relation Target entity description: The Stokes–Einstein relation is a fundamental equation in statistical physics that links the diffusion coefficient of a particle in a fluid to its size, the fluid’s viscosity, and temperature.
-
A.
Einstein–Smoluchowski relation
The Einstein–Smoluchowski relation is a fundamental equation in statistical physics that links the diffusion coefficient of particles undergoing Brownian motion to their mobility and thermal energy.
-
B.
On the Motion of Small Particles Suspended in Liquids at Rest Required by the Molecular-Kinetic Theory of Heat
"On the Motion of Small Particles Suspended in Liquids at Rest Required by the Molecular-Kinetic Theory of Heat" is Albert Einstein’s 1905 paper that provided a theoretical explanation of Brownian motion, offering strong evidence for the existence of atoms and molecules.
-
C.
Brownian motion
Brownian motion is the random, jittery movement of microscopic particles suspended in a fluid, whose explanation provided key evidence for the existence of atoms and the molecular nature of matter.
-
D.
Fokker–Planck equation
The Fokker–Planck equation is a partial differential equation that describes the time evolution of the probability density function of a stochastic (random) process, such as Brownian motion.
-
E.
Langevin dynamics
Langevin dynamics is a stochastic approach to modeling the motion of particles in a fluid by combining deterministic forces with random thermal fluctuations, often used to simulate Brownian motion and other nonequilibrium processes.
- F. None of above. chosen
Statements (49)
| Predicate | Object |
|---|---|
| instanceOf |
equation in statistical physics
ⓘ
physical law ⓘ |
| appliesTo |
Brownian particles
ⓘ
Newtonian fluids ⓘ dilute suspensions ⓘ spherical particles ⓘ |
| assumes |
continuum hydrodynamics
ⓘ
isotropic medium ⓘ low Reynolds number ⓘ no-slip boundary condition ⓘ overdamped motion ⓘ thermal equilibrium ⓘ |
| category |
diffusion
ⓘ
transport phenomena ⓘ |
| derivedFrom |
On the Motion of Small Particles Suspended in Liquids at Rest Required by the Molecular-Kinetic Theory of Heat
ⓘ
surface form:
Einstein theory of Brownian motion
Stokes law for viscous drag ⓘ |
| describes | translational diffusion of spherical particles ⓘ |
| expresses |
diffusion coefficient is directly proportional to temperature
ⓘ
diffusion coefficient is inversely proportional to fluid viscosity ⓘ diffusion coefficient is inversely proportional to particle radius ⓘ |
| field |
colloid science
ⓘ
physical chemistry ⓘ soft condensed matter physics ⓘ statistical physics ⓘ |
| hasComponentConcept |
Brownian motion
ⓘ
viscous drag ⓘ |
| hasForm | D = k_B T / (6 π η R) ⓘ |
| knownLimitation |
breaks down for supercooled liquids
ⓘ
may fail for highly crowded environments ⓘ may fail for strongly interacting colloids ⓘ |
| namedAfter |
Albert Einstein
ⓘ
George Stokes ⓘ
surface form:
George Gabriel Stokes
|
| relatesQuantity |
Boltzmann constant
ⓘ
absolute temperature ⓘ diffusion coefficient ⓘ fluid viscosity ⓘ particle radius ⓘ |
| usedFor |
characterizing colloidal dispersions
ⓘ
estimating particle size from diffusion measurements ⓘ interpreting dynamic light scattering experiments ⓘ microrheology ⓘ nanoparticle size determination ⓘ |
| validWhen |
hydrodynamic interactions are well described by continuum theory
ⓘ
particle size is much larger than solvent molecules ⓘ |
| variable |
D
ⓘ
R ⓘ T ⓘ k_B ⓘ η ⓘ |
How these facts were elicited
The pipeline generated the facts above by prompting gpt-5.1 with this entity's name + description and the instruction below.
Instruction
You are a knowledge base construction expert. Given a subject entity and a description of it, return factual statements that you know for the subject as a JSON list of dictionaries(triples), where keys must be "subject", "predicate" and "object". The number of facts may be very high, between 25 to 50 or more, for very popular subjects. For less popular subjects, the number of facts can be very low, like 5 or 10. # Requirements - If you don't know the subject at all, return an empty list. - If the subject is not a named entity, return an empty list. - Include at least one triple where predicate is "instanceOf". - Do not get too wordy. - Separate several objects into multiple triples with one object.
Input
Subject: Stokes–Einstein relation Description of subject: The Stokes–Einstein relation is a fundamental equation in statistical physics that links the diffusion coefficient of a particle in a fluid to its size, the fluid’s viscosity, and temperature.
Referenced by (2)
Full triples — surface form annotated when it differs from this entity's canonical label.
subject surface form:
George Gabriel Stokes